Remember that the position function is defined as , where D is distance. The derivative of the position funciton is velocity, . And the second derivative of the position function, and the derivative of velocity is simply acceleration, .

You are told that your vehicle is traveling at a constant deceleration of , which is the same as saying . Therefore, , where C is our initial velocity. From the problem, we want to know what our initial velocity was, which means at some time "t", our velocity will be equal to zero (the car is at rest). In mathematical terms that means: .

So, we need to know what "t". From the equation for velocity, we see that , and that the anti-derivative of this is . But, we already know that C is 10t, so: . From the problem, we know that at some time "t", the exact same "t" that our final velocity is zero, that the car will have traveled 500 meters. Therefore: . However, the cars initial position, relative to the problem, is 0, so we can say that D (which is initial position, in the same way that C is initial veloctiy) is equal to zero. Which leaves: .

Can you take it from here? If you have any questions about the reasoning used feel free to ask.